For a new setup, wool alone is not enough. In fact, u shouldn't leave ur dirty wool there, should at least change or wash every 5 to 7 days.
I think some kind of media is still necessary (or else what are all the compartments for?) Perhaps you wanna also consider Aqua Medic Cetapore (check at their website). This product is good because the surface can contains Aerobic bacts, the inside core can contains Anaerobic bacts. Anaerobic will convert Nitrates to Nitrogen (gas that will disperse out of the tank). But according to LFS, the Nitrate to Nitrogen benefit is only as secondary medium, do not rely solely on Cetapore to do the job unless you have a huge amount of them in ur sump.
If I am not so broke, I will slowly replace my Aqua Medic Bactoballs (bioballs) with Cetapore. The reason I have to do slowly is not to upset the biotope. If I am to remove all my bioballs at once, there will be A N N spikes as there aren't enough Nitrifying bacteria in the biotope to handle the bioload...
Cetapore is around $50+ a box.
Experienced bro, do correct me if I'm wrong...